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Biorthogonal multiple wavelets generated by vector refinement equation

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Science china mathematics 2007年第7期50卷 1015-1025页

作者： Song LI~(1+) Jun XIAN~2.1 department of mathematics,Zhejiang {2.,Hangzhou 31002.,china 2.department of mathematics,Sun Yat-Sen {2.,Guangzhou 5102.5,china 1. department of mathematics Zhejiang University Hangzhou 310027 China 2. department of mathematics Sun Yat-Sen University Guangzhou 510275 China

Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis. In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form $$\varphi (x) = \sum\limits_{\alpha \in \mathbb{Z}^s } {a(\alpha )\varphi (Mx - \alpha ), x \in \mathbb{R}^s } ,$$ where the vector of functions ? = (? 1, …, ? r)T is in $(L_2.(\mathbb{R}^s ))^r ,a = :(a(\alpha ))_{\alpha \in \mathbb{Z}^s } $ is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M ?n = 0. Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.

关键词： refinement equation biorthogonal multiple wavelets refinable function vector 42.40 41A10 41A15 41A2.

CJZ3,a Iomerizine derivative,modulates P-glycoprotein function in rat brain microvessel endothelial cells

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Acta Pharmacologica Sinica 2006年第4期27卷 414-418页

作者： Bian-sheng JI~2.Ling HE~3 Xiao-qu LI~4 Guo-qing LIU~(3,5) ~2.nstitute of Pharmacy,henan university,{2. 475001.china ~3department of Pharmacology,china Pharmaccutical university.Nanjing 2.0009,china:~4School of Life Sciences,Beijing Normal university,Beijing 100875,china Institute of Pharmacy Henan University Kaifeng China department of Pharmacology China Pharmaceutical University Nanjing China School of Life Sciences Beijing Normal University Beijing China

Aim:To investigate the modulatory effect of CJZ3,a lomerizine derivative,onP-glycoprotein(P-gp)function in rat brain microvessel endothelial cells(RBMEC).Methods:RBMEC were isolated and cultured in Dulbecco's modified Eagle's me-dium/F12.1:1)medium,and the amount of intracellular rhodamine 12.(Rh 12.)wasdetermined using a fluorescence spectrophotometer to evaluate the modulatoryeffect of CJZ3 on P-gp ***:The accumulation of Rh 12. was poten-tiated in a concentration-dependent manner after incubation with CJZ3 for RBMEC,but not for human umbilical vein endothelial cells(HUVEC).CJZ3 caused theaccumulation of intracellular Rh12. in a time-dependent manner and significantlydecreased the effiux of Rh 12. from the *** inhibitory effect of CJZ3 on P-gpfunction was reversible and remained for 12. min after CJZ3(2.5 μmol/L)wasremoved from the ***:CJZ3 has a potent in vitro effect on theinhibition of P-gp function.

关键词： CJZ3 P-glycoprotein blood-brain barrier

Variational construction of unbounded orbits in Lagrangian systems

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Science china mathematics 2010年第3期53卷 617-624页

作者： CHENG Chong-Qing 1, & LI Xia 2.1 department of mathematics, Nanjing {2., Nanjing 2.0093, china 2.department of mathematics, Suzhou {2. of Science and Technology, Suzhou 2.5001, china 1. department of mathematics Nanjing University Nanjing 210093 China2. Department of Mathematics Suzhou University of Science and Technology Suzhou 215001 China

We show the existence of unbounded orbits in perturbations of generic geodesic flow in T2.by a generic periodic potential. Different from previous work such as in Mather (1997), the initial values of the orbits obtain... 详细信息

关键词： positive definite Lagrangian variational method unbounded orbit

ω-Gorenstein injective modules and dimensions

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Science china mathematics 2011年第3期54卷 421-436页

作者： ZHU HaiYan1,2.& DING NanQing3 1department of mathematics, Zhejiang {2., Zhejiang 31002., china 2.0} of mathematics, Zhejiang {2. of Technology, Zhejiang 31002., china 3department of mathematics, Nanjing {2., Nanjing 2.0093, china 1. department of mathematics Zhejiang University Zhejiang 310027 China2. Department of Mathematics Zhejiang University of Technology Zhejiang 310023 China3. Department of Mathematics Nanjing University Nanjing 210093 China

Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.

关键词： Wakamatsu tilting module ω-Gorenstein injective module ω-Gorenstein injective dimension cotilting module

Regional　Man-land　System:Its　Dynamics　Characters,Structure　and　Evolutionary　Models

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Systems Science and Systems Engineering 1997年第3期7卷 84-91页

作者： ZHAO Bingdong QIN Yaochen ZHAO Qingliang department of Geography, henan university,{2.

From the point of view of dynamics, the author studies some important issues concerning the dynamics of the regional man land system. As a complex composition of man land interaction, the regional man land system is a semi open, nonlinear and partly controllable system which possesses a multi hierarchy interface structure and has its own evolutionary law. The dynamics characters, the dynamic structure and the evolutionary models of the regional man land system are all deeply discussed in this paper.

关键词： regional man land system dynamics characters dynamics structure evolutionary models.

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

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Science china mathematics 2007年第9期50卷 1251-1266页

作者： Ling-hua KONG~(1+) Ming-xin WANG~(2.3) 1 department of Applied mathematics,Dalian {2. of Technology,Dalian 11602.,china 2.department of mathematics,Southeast {2.,Nanjing 2.0018,china 3 department of mathematics,Xuzhou Normal {2.,Xuzhou 2.1116,china department of Applied mathematics Dalian University of Technology Dalian 116024 China department of mathematics Southeast University Nanjing 210018 China department of mathematics Xuzhou Normal University Xuzhou 221116 China

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.

关键词： parabolic system nonlocal sources nonlocal boundary conditions blow-up set simultaneous blow-up uniform blow-up profile 35K15 35K65

Density-functional formula for strongly correlated systems

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Progress in Natural Science:Materials International 2005年第5期15卷 395-401页

作者： WANG Huaiyu1*, HAN Rushan2.and CHEN Nanxian1(1. department of Physics, Tsinghua university, Beijing 100084,{2. 2. department of Physics, Peking university, Beijing 100871,{2.) department of Physics Tsinghua University Beijing 100084 China department of Physics Peking University Beijing 100871 China

Density functional method is applied for strongly correlated systems. Based on the assumption that the systems are composed of electrons in singly-occupied orbitals and those in doubly-occupied orbitals, a set of self-consistent equations are obtained by standard variation procedure. The equations consist of two parts. One part is to solve the wave functions of the electrons in singly-occupied orbitals and the other is to solve the wave functions of the electrons in doubly-occupied orbitals. The physical meanings of the terms appearing in the equations are discussed.

关键词： density-functional theory strongly correlated systems doubly-occupied orbital two-particle wave function self-consistent equations.

A NONLINEAR GALERKIN METHOD WITH VARIABLEMODES FOR KURAMOTO-SIVASHINSKY EQUATION

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Journal of Computational mathematics 1999年第3期17卷 243-256页

作者： Yu-jiang wu(Depadrtment of mathematics, Shanghai university, Jiadiap Shanghai 2.1800,{2. department of mathematics, Lanzhou university, Lanzhou 750000,{2.) 上海大学数学系上海

This article proposes a kind of nonlinear Galerkin methods with variable modes for the long-term integration of Kuramoto-Sivashinsky equation. It consists of finding an appropriate or best number of modes in the correction of the method. Convergence results and error estimates are derived for this method. Numerical examples show also the efficiency and advantage of our method over the usual nonlinear Galerkin method and the classical Galerkin method.

关键词： Kuramoto-Sivaskinsky equation nonlinear Galerkin method approximation convergence

Boundedness of solutions and existence of invariant tori for generalized pendulum type equation

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Chinese Science Bulletin 1997年第20期42卷 1673-1675页

作者： HUANG Hai and YUAN Rong1. Institute of mathematics, Chinese Academy of Sciences, Beijing 100080, china {2., Beijing Normal university, Beijing 100875, china Institute of mathematics Chinese Academy of Sciences Beijing China department of mathematics Beijing Normal University Beijing China

MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2. and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:

关键词： boundeduess of solutions invariant tori quasiperlodic solutions Moser’s small twist theorem.